Least Common Multiple

The least common multiple (LCM) of a set of numbers is the smallest number that each of the original numbers is a factor of. Another way to say this is that the least common multiple of a numbers is the smallest number that can be divided evenly by all the numbers we are trying to find the LCM for.

To better understand what the least common multiple is, we will first look at sort of a brute force way of finding the LCM of two numbers. This method is effective and is probably the best way to do it for small numbers since we can do it easily in our heads, however when using larger numbers it may not always work so well.

Find the LCM of 5 and 8:

We can denote the LCM of these two numbers as LCM(5,8). In order to find LCM(5,8) using our brute force method, we can simply list out a bunch of multiples of 5 and 8:

5 x 1 = 5
5 x 2 = 10
etc.

8 x 1 = 8
8 x 2 = 16
etc.

So lets say we are going to start by listing out the first 10 multiples of 5 and 8:

A Short Cut for Finding the Least Common Multiple

There is a short cut to finding the least common multiple that is similar to finding the prime factors and multiplying them together. The trick is however, you can only find the LCM or two numbers at a time.